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Some Developments in the Theory of Shape Constrained Inference. / Groeneboom, Piet; Jongbloed, Geurt.

In: Statistical Science, Vol. 33, No. 4, 2018, p. 473-492.

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Groeneboom, Piet ; Jongbloed, Geurt. / Some Developments in the Theory of Shape Constrained Inference. In: Statistical Science. 2018 ; Vol. 33, No. 4. pp. 473-492.

BibTeX

@article{e6908ed087a24523843a7da679b73350,
title = "Some Developments in the Theory of Shape Constrained Inference",
abstract = "Shape constraints enter in many statistical models. Sometimesthese constraints emerge naturally from the origin of the data. In other situations,they are used to replace parametric models by more versatile modelsretaining qualitative shape properties of the parametric model. In this paper,we sketch a part of the history of shape constrained statistical inference in anutshell, using landmark results obtained in this area. For this, we mainly usethe prototypical problems of estimating a decreasing probability density on [0,∞) and the estimation of a distribution function based on current statusdata as illustrations.",
author = "Piet Groeneboom and Geurt Jongbloed",
year = "2018",
doi = "10.1214/18-STS657",
language = "English",
volume = "33",
pages = "473--492",
journal = "Statistical Science",
issn = "0883-4237",
publisher = "Institute of Mathematical Statistics",
number = "4",

}

RIS

TY - JOUR

T1 - Some Developments in the Theory of Shape Constrained Inference

AU - Groeneboom, Piet

AU - Jongbloed, Geurt

PY - 2018

Y1 - 2018

N2 - Shape constraints enter in many statistical models. Sometimesthese constraints emerge naturally from the origin of the data. In other situations,they are used to replace parametric models by more versatile modelsretaining qualitative shape properties of the parametric model. In this paper,we sketch a part of the history of shape constrained statistical inference in anutshell, using landmark results obtained in this area. For this, we mainly usethe prototypical problems of estimating a decreasing probability density on [0,∞) and the estimation of a distribution function based on current statusdata as illustrations.

AB - Shape constraints enter in many statistical models. Sometimesthese constraints emerge naturally from the origin of the data. In other situations,they are used to replace parametric models by more versatile modelsretaining qualitative shape properties of the parametric model. In this paper,we sketch a part of the history of shape constrained statistical inference in anutshell, using landmark results obtained in this area. For this, we mainly usethe prototypical problems of estimating a decreasing probability density on [0,∞) and the estimation of a distribution function based on current statusdata as illustrations.

U2 - 10.1214/18-STS657

DO - 10.1214/18-STS657

M3 - Article

VL - 33

SP - 473

EP - 492

JO - Statistical Science

T2 - Statistical Science

JF - Statistical Science

SN - 0883-4237

IS - 4

ER -

ID: 47712385